Teaching objectives
Working with coins or counters develops spatial perception, planning and an understanding of rules — and it's fun! In this lab the student has to transform one configuration of coins into another using different procedures: jumps, slides and flipping coins, across 3 different types of grid.
What is learned
The student starts from a coin position and must reach another one. Each challenge teaches how to plan a sequence of steps towards a goal, to read a position and to reason backwards from the target. The 19 rooms range from a single simple move to the final flipping challenge on a hexagonal grid.
- Move coins under different rules: free (to any empty cell), to an adjacent cell, sliding through contiguous empty cells (without jumping), and jumping over another coin.
- Respect placement constraints, such as "when you drop it, the coin must end up touching at least two others".
- Transform shapes: flip a pyramid, form a triangle or a hexagon, turn a square into a triangle.
- Swap two groups of coloured coins (leapfrog-type problems).
- Solve within a limited number of moves: look for the efficient solution, not just any solution.
- Flip coins (heads ↔ tails) to reach a pattern, with three different effects: only the coin you tap, it and its neighbours (Lights Out style), or the lines that pass through it.
- Work on two grids: square (4 neighbours) and hexagonal (6 neighbours), where a cell belongs to three lines.
Key mathematical ideas
- Planning and search: each challenge is a problem of states and moves; solving it means finding a path from the start to the goal.
- Efficiency: the "minimum number of moves" introduces the idea of an optimal solution versus just any solution.
- Parity and invariants (in the flips): the order of taps does not matter, and tapping the same coin twice is the same as not tapping it — a first intuition of arithmetic modulo 2.
- Geometry of the grid: neighbourhood, lines and symmetry on square and hexagonal grids.
How it is organised
- Rooms 1-6 — Moving with the "touch two" rule, slides and jumps: rescue trapped coins and rearrange clusters.
- Rooms 7-9 — Transform one shape into another in a fixed number of moves; some with a hidden goal that appears as a hint after several attempts or on request.
- Rooms 10-14 — Colour swaps, leapfrog-type jumps and moving the pieces to the opposite corner or upwards.
- Rooms 15-19 — Flipping coins (heads/tails) with the three effects, up to the final challenge on a hexagonal grid with staged hints.
Each challenge shows the current and the target position side by side (one above the other on mobile). If a move breaks a rule, the game explains in words why (for example: "there the coin doesn't touch two"). Some rooms offer a hint that replays the first moves of a solution, at the cost of a point.
Room-by-room contents
Room 1 · Four coins
First challenge on a hexagonal grid. You move a single coin to go from the starting cluster to the final one; the rule requires that, when you drop it, it ends up touching at least two other coins. Solved in 2 moves.
Student tasks
- Tap a coin and then a cell where it ends up touching two others.
- Reach the final configuration in 2 moves.
Room 2 · Free the prisoner
The red coin is surrounded. By sliding through contiguous empty cells (no jumping) and keeping every moved coin touching two others, you have to get it out to its place. Minimum 3 moves.
Student tasks
- Slide coins through the empty gaps.
- Bring the red coin to its target cell.
Room 3 · Flip the pyramid
A 10-coin pyramid must be turned upside down. Free movement, each coin must end up touching two, and only 3 moves are allowed.
Student tasks
- Plan which 3 coins to move.
- Invert the pyramid in 3 moves.
Room 4 · Form a triangle
Starting from a compact group, form a triangle by moving only 2 coins; each must touch two when dropped.
Student tasks
- Choose the 2 coins to move.
- Form the triangle in 2 moves.
Room 5 · Form a triangle
A variant with fewer coins: again two moves to make the triangle, touching two when placing each coin.
Student tasks
- Solve the triangle in 2 moves.
Room 6 · Free two prisoners
Now two red coins are trapped. By sliding (no jumping) and touching two, you must get both out. Minimum 5 moves.
Student tasks
- Free the two red coins in 5 moves.
Room 7 · Square into triangle
On a square grid, transform the figure into a triangle in 2 moves. The goal is hidden: it appears as a hint after several attempts or on request.
Student tasks
- Work out the final figure and achieve it in 2 moves.
- Ask for the hint if needed.
Room 8 · Triangle into square
The reverse challenge: triangle to square in 3 moves, also with the goal hidden until you ask for the hint.
Student tasks
- Make the square in 3 moves.
Room 9 · Form a hexagon
Rearrange 12 coins to form a hexagon. Free movement; 6 moves are needed, one for each misplaced coin.
Student tasks
- Move the 6 extra coins to their place.
- Form the hexagon in 6 moves.
Room 10 · Swap yellow and blue
On a 3×3 with the centre empty, swap the yellow and blue coins by sliding them as in a sliding-tile puzzle. Minimum 12 moves.
Student tasks
- Slide the coins until the two colours are swapped.
Room 11 · Leapfrog
The classic frogs-and-toads on a row: two blue and two yellow separated by a gap. By sliding and jumping over a coin, you must swap them. Minimum 8 moves.
Student tasks
- Swap the two groups without getting stuck.
Room 12 · Swap on two rows
A two-row (2×4) version of the colour swap with slides and jumps. Minimum 10 moves.
Student tasks
- Swap yellow and blue in 10 moves.
Room 13 · To the opposite corner
Six pieces in one corner of a 4×4 board must reach the opposite corner by moving to a neighbouring cell or jumping. At most 12 moves. A hint replays the first steps of a solution.
Student tasks
- Bring the 6 pieces to the opposite corner in 12 moves.
- Use the hint if you get stuck.
Room 14 · Jump upwards
Only jumping over a neighbouring coin is allowed. You must move the group upwards on the hexagonal grid. At most 10 moves.
Student tasks
- Move the coins upwards by jumping, in 10 moves.
Room 15 · Flip three at a time
First flipping challenge (heads ↔ tails). On a row, tapping a coin flips it and its neighbours (3 at once). You must leave them all showing the yellow side in 2 taps.
Student tasks
- Make all the coins show the yellow side in 2 taps.
Room 16 · Flip the row and column
On a square grid, tapping a coin flips its whole row and column. Goal: all yellow in 3 taps.
Student tasks
- Leave every coin yellow in 3 taps.
Room 17 · Make the pattern
Flipping (the coin and its neighbours) on a hexagonal grid to reproduce a specific pattern of heads and tails. 6 taps.
Student tasks
- Reproduce the target pattern in 6 taps.
Room 18 · All tails
Every coin starts tails-up. On the hexagonal grid, tapping one flips the 3 lines through it (the horizontal and two oblique). You must turn them all to the yellow side in 4 taps: the hardest challenge this board allows.
Student tasks
- Turn every coin yellow in 4 taps.
Room 19 · The 3 lines
The final challenge: the same 3-line effect on a larger hexagonal board; solved in 5 taps. If you get stuck, a staged hint first shows the first 2 taps and then the first 3.
Student tasks
- Solve the pattern in 5 taps.
- Lean on the staged hints if needed.
Rooms to project
The most striking ones to show and discuss in class.